Motivated by market design for electric power systems, we consider a model where a finite number of producers compete to meet an infinitely divisible but inelastic demand for the product. Each firm is characterized by a production cost that is convex in the output produced, and firms act as profit maximizers. We consider a uniform price market design that uses supply function bidding [22]: firms declare the amount they would supply at any positive price, and a single price is chosen to clear the market. We are interested in evaluating the impact of price anticipating behavior both on the allocative efficiency of the market, and on the prices seen at equilibrium. We show that by restricting the strategy space of the firms to parameterized supply functions, we can provide upper bounds on both the inflation of aggregate cost at the Nash equilibrium relative to the socially optimal level, as well as the markup of the Nash equilibrium price above the competitive level: as long as N> 2 firms are competing, these quantities are both upper bounded by 1 + 1/(N − 2). This result holds even in the presence of asymmetric cost structure across firms. We also discuss several extensions, generalizations, and related issues. 1

Most US consumers are charged a near-constant retail price for electricity, despite substantial hourly variation in the wholesale market price. This paper evaluates a randomized experiment that exposed households to hourly real time pricing (RTP) and applies the demand estimates to counterfactual simulations in a structural model of the Pennsylvania-Jersey-Maryland electricity market. The model includes a di¤erent approach to the problem of multiple supply function equilibria: I non-parametrically estimate unobservables that rationalize past bidding behavior and use learning algorithms to select …rms ’ counterfactual supply functions. This routine is nested as the second stage of a static entry model that captures an important institution called the Capacity Market, which acts in equilibrium as a minimum constraint on system capacity and transfers the shadow price to capacity owners. There are three central results. First, the experiment’s net e¤ect on consumer behavior was energy conservation during peak hours, not substitution from peak to o¤-peak. Second, large scale RTP would actually increase wholesale electricity prices in peak hours, contrary to predictions from short-run models, while decreasing Capacity Market prices and total entry. Third, although the increased demand elasticity from RTP theoretically reduces producers’ market power, in practice this would be a second-order channel of e ¢ ciency gains. I …nd that through RTP’s combined e¤ects on electricity and Capacity prices, producers ’ and retailers’ pro…ts would be slightly lower, but consumers would realize large welfare gains.

Center conducting research on challenges facing the electric power industry and educating the next generation of power engineers. More information about PSERC can be found at the Center’s website:

Most US consumers are charged a near-constant retail price for electricity, despite substantial hourly variation in the wholesale market price. The Smart Grid is a set of emerging technologies that will facilitate "real-time pricing " for electricity and increase price elasticity of demand. This paper simulates the e¤ects of this increased demand elasticity using counterfactual simulations in a structural model of the Pennsylvania-Jersey-Maryland electricity market. The model includes a di¤erent approach to the problem of multiple equilibria in multi-unit auctions: I nonparametrically estimate unobservables that rationalize past bidding behavior and use learning algorithms to move from the observed equilibrium counterfactual bid functions. This routine is nested as the second stage of a static entry game that models the Capacity Market, an important element of market design in some restructured electricity markets. There are three central results. First, I …nd that an increase in demand elasticity could actually increase wholesale electricity prices in peak hours, contrary to predictions from short run models, while decreasing Capacity Market prices and total entry. Second, although the increased demand elasticity from the Smart Grid reduces producers’market power, in practice

A finite number of sellers (n) compete in schedules to supply an elastic demand. The costs of the sellers have uncertain common and private value components and there is no exogenous noise in the system. A Bayesian supply function equilibrium is characterized; the equilibrium is privately revealing and the incentives to acquire information are preserved. Price-cost margins and bid shading are affected by the parameters of the information structure: supply functions are steeper with more noise in the private signals or more correlation among the costs parameters. In fact, for large values of noise or correlation supply functions are downward sloping, margins are larger than the Cournot ones, and as we approach the common value case they tend to the collusive level. Private information coupled with strategic behavior induces additional distortionary market power above full information levels and welfare losses which can be counteracted by subsidies. As the market grows large the equilibrium becomes price-taking, bid shading is 2 of the order of 1/n, and the order of magnitude of welfare losses is 1/n. The results

The single clearing-price auction is perhaps the most basic building block of markets. Buyers submit demand bids and sellers submit supply offers. The auctioneer then forms the aggregate supply and demand curves, and finds the clearing price at which supply and demand balance; that is, where the supply and demand curves cross. All demand bids above the clearing price and all supply offers below the clearing price are accepted. The winning buyers pay the clearing price and the winning sellers are paid the clearing price for their accepted quantities. The single clearing-price auction is important because of its simplicity and effectiveness at answering the most basic questions: who should get the goods, who should produce the goods, and at what prices. Based on each market participant’s expressed preference, the single clearing-price auction awards the goods to all consumers who value the goods more than the cost (the clearing price) and the goods are produced by all suppliers who have a cost less than their payment (the clearing price). In this way, the clearing-price auction maximizes gains from trade: consumption comes from demand with the highest values and production comes from supply with the lowest cost. This is perhaps the most celebrated result in economics. It should be no surprise that the single clearing-price auction is the centerpiece of restructured electricity markets. Most electricity systems use the single clearing-price auction in many places. The most important application is the spot energy market, which is a real-time market to determine the price of electricity at a particular time and location.